The Elements of the Differential Calculus: Comprehending the General Theory of Curve Surfaces, and of Curves of Double CurvatureCarey, Lea & Blanchard, 1833 - 255 σελίδες |
Περιεχόμενα
| 1 | |
| 9 | |
| 15 | |
| 26 | |
| 32 | |
| 34 | |
| 40 | |
| 46 | |
| 116 | |
| 117 | |
| 119 | |
| 120 | |
| 122 | |
| 123 | |
| 124 | |
| 125 | |
| 52 | |
| 58 | |
| 83 | |
| 84 | |
| 88 | |
| 89 | |
| 94 | |
| 95 | |
| 96 | |
| 99 | |
| 100 | |
| 101 | |
| 102 | |
| 103 | |
| 104 | |
| 107 | |
| 108 | |
| 109 | |
| 111 | |
| 113 | |
| 114 | |
| 126 | |
| 128 | |
| 149 | |
| 150 | |
| 155 | |
| 158 | |
| 161 | |
| 167 | |
| 170 | |
| 177 | |
| 180 | |
| 182 | |
| 196 | |
| 201 | |
| 212 | |
| 215 | |
| 227 | |
| 229 | |
| 235 | |
| 241 | |
Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
abscissa Anal ax² axes axis become infinite binomial theorem chapter circle condition conical surface constant corresponding cusp d³y d³z deduced determine differential coefficient dx dx dx dy dx dx² dx³ dy dx dy dy dy dy dz dy² dy³ dz dz equa example expression f(x+h fraction generatrix Geom given hence hyperbola imaginary independent variable intersection lines of curvature logarithm maxima and minima maximum minima values minimum normal numerator and denominator ordinate osculating osculating circle particular value plane curve positive power of h proposed point radical radii radius of curvature render represent Required the value second order sine spiral substituting subtangent suppose tangent plane Taylor's theorem term tion true development values of h vanish
Δημοφιλή αποσπάσματα
Σελίδα ii - SON, in the office of the Clerk of the Southern District of New. York.
Σελίδα 12 - It was also shown in the same article, that the differential of the sum of any number of functions is equal to the sum of their...
Σελίδα 129 - Fig. 52, the point A be kept fixed and the point B moved along the curve until it coincides with A, the secant AB becomes a tangent to the curve at the point A. Two curves are said to be tangent to each other at a point when they have a common tangent at that point. If a straight line is tangent to a plane curve, the tangent will lie in the plane of the curve. This is evident since the secant...
Σελίδα 28 - If u represent a function of x which it is possible to develop in a series of positive ascending powers of that variable, then will that development be where the brackets indicate the values which the inclosed functions assume when x equals zero.
Σελίδα 3 - If both members of the last equation be divided by h, we shall have u' — u •which expresses the ratio of the increment of the function to that of the variable.
Σελίδα i - ELEMENTS OF THE DIFFERENTIAL CALCULUS ; comprehending the General Theory of Curve Surfaces, and of Curves of Double Curvature. Revised and corrected by MICHAEL O'SHANNESSY, AM 1 vol.
Σελίδα 10 - Zdv -\- vdz, butt' = wy; therefore, by (3), do = ydw + wyd ; consequently, by substitution, iln = zydw + ziody + wydz . . . (4), and it is plain that in this way the differential may be found, be the factors ever so many ; so that, generally, to differentiate a product of several functions of the same variable, we must multiply the differential of each factor by the product of all the other factors, and add the results.
Σελίδα 16 - The differential of the logarithm of a function is equal to the differential of the function, divided by the function itself.
Σελίδα 201 - As an example, let it be required to find the equation of the inferior surface of a winding staircase, the aperture or column round which it winds being cylindrical.
Σελίδα 143 - F' (x) is the trigonometrical tangent of the angle between the axis of x and the tangent to the curve at the point (x, y). Art. 38. Let...